Liu, Jiangguo; Popov, Bojan; Wang, Hong; Ewing, Richard E. Convergence analysis of wavelet schemes for convection-reaction equations under minimal regularity assumptions. (English) Zbl 1091.65096 SIAM J. Numer. Anal. 43, No. 2, 521-539 (2005). The initial value problem for the multidimensional linear convection-reaction equation is considered. For a numerical solution of this problem the authors propose one of characteristic methods – the Eulerian-Lagrangian localized adjoint method. Then error estimates for the numerical schemes are formulated and proved. The estimates are obtained under some minimal regularity assumptions in the L-norm and in a Besov space. Numerical experiments illustrate the theoretical results. Reviewer: Ivan Secrieru (Chişinău) Cited in 1 Document MSC: 65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 76M20 Finite difference methods applied to problems in fluid mechanics 35L15 Initial value problems for second-order hyperbolic equations 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs Keywords:convection-reaction equation; adjoint equation; characteristics method; error estimates; convergence rate; Eulerian-Lagrangian method; wavelet method; numerical experiments PDFBibTeX XMLCite \textit{J. Liu} et al., SIAM J. Numer. Anal. 43, No. 2, 521--539 (2005; Zbl 1091.65096) Full Text: DOI